Although I guess if you really want to be anal, the heavier object hits very slightly first because the earth is accelerating up to the heavier object. So two earth sized masses would fall toward each other faster than a ping pong ball and the earth.

The equation of gravitational law shows it
F = GMm/r^2 where F is force applied due to gravitation by earth, G is a constant, M is the mass of the earth, m is the mass of the thrown object and r is the radius of the earth and from the law distancebetween the centre of two objects.

F = ma
therefore a = F/m = which here is g.
thus g is equal for all objects. may it be anything. now what mcah5 explained is the gravitational force applied by object on earth. the heavy celestial bodies apply gavitational force on earth due to which the gravitational force on earth due to object becomes negligible.